Chirp Waveform Generation Using Digital Samples

Abstract

This paper describes two methods of generating an analog frequency-modulated waveform by the use of a small number of digital samples of the "chirp" waveform. The number of digital samples required is a function of the time-bandwidth product. For certain values of time-bandwidth product, this type of signal generation becomes extremely efficient. Several proofs are offered which show how to select "optimum" values of time-bandwidth products. Two hardware implementations are suggested. One is based on the use of modulo arithmetic and a small stored memory table. The second method utilizes the inherent signal symmetries available if "optimum" time-bandwidth products are selected. The symmetrical signal patterns are stored in recirculating reversible shift registers which can be read out at high speeds.